Problem: Divide. Write the quotient in lowest terms. $\dfrac{3}{5} \div 2\dfrac1{2} = $
Solution: First, let's rewrite $2\dfrac1{2}$ as a fraction: $\dfrac{3}{5} \div 2\dfrac1{2} =\dfrac{3}{5} \div \dfrac{5}{2}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac52$ is $\dfrac2{5}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{3}{5} \div \dfrac{5}{2}=\dfrac{3}{5}\times\dfrac2{5}$ $=\dfrac{3\times 2}{5\times 5}$ $=\dfrac{6}{25}$